Cermet materials, consisting of finely divided ceramic and metallic components, combine to a certain degree the advantageous characteristics of the metals, e.g., their good electrical and thermal conductivity and the advantageous properties of the ceramics, e.g., their good corrosion resistance. For this reason, Cermet materials consisting of refractory oxides, e.g., alumina or zirconia, and refractory metals, e.g., molybdenum or tungsten, have proved highly suitable for making structural parts in contact with molten metals. In many instances, however, there is the problem of how to give such cermet parts a nonmetallic surface coating. The known methods for producing such coatings, e.g., by spraying or sintering, are not satisfactory because the coating is not sufficiently firmly bonded to the base. These deficiencies are overcome by the present invention.